A geometric analysis of diffusion tensor measurements of the human brain

The degree of diffusion tensor anisotropy is often associated with the organization of structural tissues such as white matter. Numerous measures of diffusion anisotropy have been proposed, which could lead to confusion in interpreting and comparing results from different studies. In this study, a new method for representing the diffusion tensor shape, called the three-phase (3P) plot, is described. This is a graphical technique based upon a barycentric coordinate system, which weights the tensor shape by a combination of linear, cylindrical, and spherical shape factors. This coordinate system can be used to map and potentially segment different tissues based upon the tensor shape. In addition, the 3P plot can be used to examine the shape properties of existing measures of diffusion anisotropy. In this paper, the 3P plot is used to compare four well-known anisotropy measures: the anisotropy index, the fractional anisotropy, the relative anisotropy, and the volume fraction. Computer simulations and diffusion tensor images of normal brains were obtained to study the properties of this new mapping technique. Magn Reson Med 44:283-291, 2000.